Hi Stephie -
<<"If it's possible, would Lucerne or Interlaken be a fastest and convenient route to Italy?
Are dogs allowed on the boats and cable cars?">>
Indeed, I have seen dogs in restaurants, on trains, on boats and on cableways ( at least, the kind with a large cabin). Don't think it would work on a chair lift. ;-)
However, ALL of the dogs have been extremely well-behaved. In a restaurant, they get under the table and stay there. On a train, they stay at the feet of the owner or, on some trains, under the seat. They are quiet. They don't move around or bother other passengers. Ifyour dog does not have civilized Swiss manners, you will get some nasty looks, at a minimum.
How tall is your dog at the shoulder? 19kg is not extremely large, but you might well find that a dog that size occupies the space belonging to another passenger in some way. That could be a problem, especially on crowded trains. Many buses have a place near the center doors large enough to accomodate a wheel chair, sometimes bicycles. You could sit or stand ( for short distances) there to find space for your dog.
Since seating in some trains has two seats facing each other to make a set of four seats. The space betwen those four seat is for the legs and feet of four passengers. On a full train, that type of seating, which is not universal, could be an issue.
For long distance travel on trains, First Class will give everyone more space. And, the cars may well not be full.
You can get to Italy from anywhere in Switzerland. ;-) To learn about the fastest routes, which can include passing through Luzern, Interlaken, or any other place, use the time table:
If you wish to go through a certain city, enter it in the "via" box.
Enter your starting point in Switzerland and your destination in Italy. For Milano and onward to Venice various routes are convenient, depending on where you start. Common routes by train are via the Gotthard Pass ( easy from Zürich or Luzen, and via the Simlon from Brig, easy from Interlaken. The time table will give you the fastest route by default, and allows you to see the stops en route.
In order to visualize the geography, as you think about routes and alternatives, to help you understand the train routes and the relative locations of the cities, this map is very helpful:
Zoom in and you will see the train lines. Play with the menu entries under "Traffic."
Weather during your trip will not resemble Singapore!
Check out the links on these pages:
Of the 3 mountains that you name near Luzern, Pilatus would have the least open spaces that your dog might enjoy. The Rigi is at lower altitude and has more fields/meadows and general openness. Walking the trails near the top of the Rigi and Rigi-Kaltbad could be nice, if there is no snow on the ground that might make the trails difficult.